Question

How to solve x when give the derivative?

Can someone please explain to me how to do question6 f? Thanks!

Answer 1

`5/8`

Explanation:

Given equation is,

`f(x)=3(2x-1)^2=12x^2 -12x+3`

So, `f'(x) =24x-12`

If , `f'(x)=3`

then, `3=24x-12`

or, `24x=15`

so, `x=5/8`

Answer 2

The trick is to first do the derivative, and then solve for x. In this case, `x=5/8=0.625`

Explanation:

First we write the base expression:

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

Now, we differentiate. For differentiation of the section in the parentheses, you first differentiate as if it were one value, and then multiply the equation by the differential of the contents of the parentheses:

`f'(x)=3*2(2x-1)*d/dx (2x-1)`

`f'(x)=6(2x-1)*2 rArr f(x)=12(2x-1)=24x-12`

now that we have the equation, we can solve for sub-question f. If `f'(x)=3`, we can plug that into our equation:

`3=24x-12 rArr 24x=15 rArr x=15/24`

`15/24` simplifies to `color(red)(5/8)` due to a common factor of 3. In decimal form, that is `color(red)(0.625)`