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



Answered question


Compute f'(3), where f(x)=x28x.

Answer & Explanation

Nathalie Redfern

Nathalie Redfern

Skilled2021-05-20Added 99 answers

Step 1
For a function f(x) its derivative is given by the definition limh0f(x+h)f(x)h. For some standard functions like xn 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 xn,nq0 is equal to nxn1.
Step 2
Given function is f(x)=x28x. Find its first derivative and then substitute x=3 to find f'(3).
Hence, for the given function f'(3)=−2.

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