Determine the linear Lagrange interpolating polynomial that passes through the points (2,4) and (5,1). Please explain all steps so I can understand how you got your answer.

Determine the linear Lagrange interpolating polynomial that passes through the points (2,4) and (5,1). Please explain all steps so I can understand how you got your answer.

Let f(x)=x^2−8x. To prove that limx→4f(x)=−16, we proceed as follows. Given any ϵ>0, we need to find a number δ>0 such that if 0<|x−4|<δ, then |(x2−8x)−(−16)|<ϵ. What is the (largest)...

Suppose that an object moves along an s-axis so that its location is given by s(t)=t^2+8t at time t. (Here s is in meters and t is in seconds. a) Find the average velocity of the object in...

The tangent line to y=f(x) at (−8,−9) passes through the point (7,7). Compute the following. a) f(-8) b) f'(-8)

Let f(x)=−5x+(−5). Find the largest δ so that |f(x)−f(a)|<ϵ when |x−a|<δ. δ=________

Find dy/dx in terms of x and y if x^9+y^2=√2 dy/dx=_____

The top of a 17 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate of 4 feet per second. How fast is the bottom of the ladder sliding along the ground when the bottom...

How fast is the ladder moving toward the wall when the top of the ladder is 6 feet off ghe ground?

Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 9 mi^2/hr. How rapidly is radius of the spill increasing when the area is 9 mi^2?

Find the derivative of w=(√t+5)^76 dw/dt=______

Find the derivative of f(x)=√[6−sinx/2−cosx] The square root is over everything. f'(x)=____

Find f if f′(x)=6x−[3/x^4], x>0, and f(1)=3. f(x)=_____

If you have 140 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose? Area=_______

Evaluate the following limit lim [8−√x]/[8+√x] ...

Find the inflection points of f(x)=8x^4+110x^3−42x^2+13. (Give your answers as a comma separated list) Inflection Points=_______

Find all critical points of the function f(x)=x^3+7x^2−7x−3. If there is more than one critical point, list them in descending order and separate them by commas. Critical...

Find f if f′′(x)=sin x + cos x, f′(0)=3, and f(0)=2. f(x)=_____

The point P(0.2,15) lies on the curve y=3/x. Let Q be the point (x,3/x) a.) Find the slope of the secant line PQ for the following values of x. If x=0.3, the slope of PQ is: If...

Find all critical values for the function f(r)=[(3r)/(6r^2+10)] and then list them (separated by commas).

Find dy/dx in terms of x and y if 2xy+4x+y=6. dy/dx=____

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