436 Answered Questions for the topic Derivative

Derivative Calculus

12/30/12

Consider f(x)=x^2/x^2+a, a>0. Determine the effect on the graph of f if a is varied?
consider f(x)=x^2/x^2+a, a>0. Determine the effect on the graph of f if a is varied Does this mean that... A) Each y value is multiplied by a B) As a increases, the vertical tangent lines move... more
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12/30/12

Given f(x)= -1/x, find all c in the interval [-3, -1/2] that satisfies the Mean Value Theorem?
Given f(x)= -1/x, find all c in the interval [-3, -1/2] that satisfies the Mean Value Theorem. How do you solve this problem and which is the right answer choice and why? a) c= -√3/2 b) + & -... more
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Derivative Calculus

12/29/12

Let f"(x)=4x^3 -2x and let f(x) have critical values -1, 0, and 1.?
Let f"(x)=4x^3 -2x and let f(x) have critical values -1, 0, and 1. Determine which critical values give a relative maximum How do you figure this out and which is the right answer and why? a) -1 b)... more
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Derivative Calculus Graph Maximum

12/29/12

Which statement is not true of the graph f(x)= (x+1)(x-3)^2?
How do you solve this problem? Which is the right answer and why? a) f has a relative maximum at (1/3, 256/27) b) f has a point of inflection at (3,0) c) f has an intercept at (3,0) d) f has a... more
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12/29/12

f(x)=(x+2)^3 -4 The point (-2,-4) is which of the following?
How do you solve this problem? Which is the right answer and why? a. An absolute maximum b. An absolute minimum c. A critical point but not an extremum d. Not a critical point e. none of these
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12/29/12

Let f(x) be a polynomial function such that f(-2)=5, f'(-2)=0 and f"(-2)=3. The point (-2,5) is which of the following for the graph of f?
How do you figure out this problem. Which is the correct answer choice and why? a) relative maximum  b) relative minimum  c) intercept d) inflection point e) none of these
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12/29/12

Let f(x) be a polynomial function such that f(4)= -1, f'(4)=2 and f"(4)=0. If x<4, then f"(x)<0 and if x>4, then f"(x)>0.

The point (4,-1) is which of the following for the graph of f? How do you figure out this problem. Which answer choice is right and why? a) relative maximum b) relative minimum c) critical... more
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Derivative Calculus Intervals

12/29/12

State why Rolle's Theorem does not apply to f(x)= x^(2/3) on the interval [-1,1]
Please explain how to figure out the problem. Which answer is correct and why? a) f is not continuous on [-1,1] b) f is not defined on the entire interval c) f is not differentiable at x=0 d)... more
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12/29/12

Find the value(s) of c guaranteed by Rolle's Theorem for f(x)= x^2 +3x on [0,2]
How do you solve this and which answer choice is right and why? a) c= -3/2 b) c= 0,3  c) Rolle's Theorem does not apply as f is not continuous on [0,2] d) Rolle's Theorem does not apply as f(0)... more
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12/29/12

Use the graph of f(x)= x^2/x^2-4 to determine on which of the following intervals Rolle's Theorem applies?
How do you figure out this problem and which answer is right and why? Choices: a) [0,3] b) [-3,3] c) [-3/2,3/2] d) [-2,2] e) none of these
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Derivative Calculus

11/25/12

the derivative of y=sin(5x)cos(2x)
Find the derivative of the function. 
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