We are given f ( x ) = 8 x 2 and f \' ( x ) = 16 x . Please fill in the question

Question

We are given f(x) = 8x2 and f'(x) = 16x. Please fill in the question marks.

a) Find the instantaneous rate of change of f(x) at x = 3.

We are told that for f(x) = 8x2, f'(x) = 16x. We want to find the instantaneous rate of change of f(x) at x = 3.

The instantaneous rate of change of f(x) is given by f'(x). Thus, at x = 3, the instantaneous rate of change of f(x) is given by the following.

f' (??)=16(??)

=??

b) Find the slope of the tangent to the graph of y = f(x) at x = 3.

We are told that for f(x) = 8x2, f'(x) = 16x. We want to find the slope of the tangent to the graph of y = f(x) at x = 3. The slope of the tangent to the graph of y = f(x) is given by f'(x).Thus, at x = 3, the slope of the tangent to the graph of y = f(x) is given by the following.

f' (??)=16(??)

=??

Explanation / Answer

The instantaneous rate of change of f(x) is given by f'(x).

here f(x) = 8x2

andf'(x) = 16x

at x = 3, the instantaneous rate of change of f(x) is given by f' (3)=16(3) = 48

b) The slope of the tangent to the graph of y = f(x) is given by f'(x)

we want to find slope at x = 3

hence The slope of the tangent to the graph of y = f(x) is given by f'(x)

f' (3)=16(3) = 48

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