Yulia

2021-05-19

Compute f'(3), where $f\left(x\right)={x}^{2}-8x$ .

Nathalie Redfern

Skilled2021-05-20Added 99 answers

Step 1

For a function f(x) its derivative is given by the definition$\underset{h\to 0}{lim}\frac{f(x+h)-f\left(x\right)}{h}$ . For some standard functions like $x}^{n$ the derivative is known so there is no need to find derivative of functions written in terms of standard functions.

Use one property of derivatives (f(x)+g(x))′=f'(x)+g'(x). Use another property of derivatives (cf(x))′=cf'(x). Use the derivative of${x}^{n},n\ne q0$ is equal to $n{x}^{n-1}$ .

Step 2

Given function is$f\left(x\right)={x}^{2}-8x$ . Find its first derivative and then substitute x=3 to find f'(3).

$f\left(x\right)={x}^{2}-8x$

$f}^{\prime}\left(x\right)={({x}^{2}-8x)}^{\prime$

$={\left({x}^{2}\right)}^{\prime}-{\left(8x\right)}^{\prime}$

=2x-8(x)'

=2x-8

f'(3)=2*3-8

=-2

Hence, for the given function f'(3)=−2.

For a function f(x) its derivative is given by the definition

Use one property of derivatives (f(x)+g(x))′=f'(x)+g'(x). Use another property of derivatives (cf(x))′=cf'(x). Use the derivative of

Step 2

Given function is

=2x-8(x)'

=2x-8

f'(3)=2*3-8

=-2

Hence, for the given function f'(3)=−2.

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function

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