Find the derivative

Question

Find the derivative of f(x) = 11x2 + 5x at x = 9.

243
223
203
-243

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Find the derivative of f(x) = 3 divided by x at x = 1.

-3
-1
1
3

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The position of an object at time t is given by s(t) = -4 - 2t. Find the instantaneous velocity at t = 6 by finding the derivative.

 

 

Answer 1

I think you meant f(x) = 11x² + 5x. Let's find its derivative:

 

f'(x) = 2(11)x + 5

f'(x) = 22x + 5

 

At x = 9, that's:

 

f'(9) = 22(9) + 5

f'(9) = 198 + 5

f'(9) = 203

 

 

We can re-write f(x) = 3/x as f(x) = 3x^-1. That's because a^-n = 1/aⁿ. Let's find its derivative:

 

f'(x) = -1(3x^-2)

f'(x) = -3x^-2

f'(x) = -3/x²

 

At x = 1, that's:

 

f'(1) = -3/1²

f'(1) = -3/1

f'(1) = -3

 

 

The derivative of s(t) is:

 

s'(t) = 0 - 2

s'(t) = -2

 

At t = 6, that's just:

 

s'(6) = -2