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Solve the given problems.Find $f(x)$ if $f^{\prime}(x)=4 x-5$ and $f(-1)=10$.

$f(x)=2 x^{2}-5 x+3$

Calculus 1 / AB

Chapter 25

Integration

Section 2

The Indefinite Integral

Integrals

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Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

00:58

For the functions in Probl…

00:59

00:32

Find $f^{-1}(x)$ for each …

01:34

00:53

Solve.Let $f(x)=|2 x+4…

01:17

Find $f$$$f^{\prime}(x…

00:24

Find $f(\mathbf{0 )} \text…

00:42

$$\text { If } f(x)=x^{2}-…

Let $f(x)=|5-4 x| .$ Find …

00:41

Find $f(3)$ if $f(x)=-4 x^…

All right. So here we have a function f of X equals 10 x minus X squared, and we're being asked to find what effort five is. So all we need do is plug in five. An easy way to kind of remember how to do that is that that X got replaced with the five. So we should replace all of the exits with fives. Remember that this is not 105 because when we say 10 X, we actually mean 10 times X, it's gonna be 10 times five. And we're denoting multiplication with that little dot now instead of an ex because we're using variables. So it gets a little bit confusing if we have an ex meaning of variable. And we have ex meaning multiplication. So we have 10 times five minus five squared. We know 10 times five is 50 and five squared is 25. So 50 minus 25 is equal to 25 so f of five equals 25

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For the functions in Problems $10-14,$ find $f(5)$.$$f(x)=10 x-x^{2}$$

For the functions in Problems $10-14,$ find $f(5)$.$$f(x)=2 x+3$$

Find $f^{-1}(x)$ for each function.$$f(x)=x+5$$

Find $f^{-1}(x)$ for each function.$$f(x)=\frac{2 x+3}{5 x+4}$$

Solve.Let $f(x)=|2 x+4| .$ Find all $x$ for which $f(x)=10$

Find $f$$$f^{\prime}(x)=5 x^{4}-3 x^{2}+4, \quad f(-1)=2$$

Find $f(\mathbf{0 )} \text { and } f(2)$ for each of the given exponential f…

$$\text { If } f(x)=x^{2}-2 x+5, \text { find } f(-4)$$

Let $f(x)=|5-4 x| .$ Find all values of $x$ for which $f(x)=11$

Find $f(3)$ if $f(x)=-4 x^{2}+5 x$

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