find the intervals in which the function is decreasing and increasing?

Question

f(X)= 2x^2+8x-10

find the intervals on which the function is increasing and the intervals in which the function is decreasing?


Please explain. thank you

Answer 1

First find the derivative of f using the power rule

f(x) = 2x^2 + 8x -10
f(x) = 4x + 8

Then set the derivative equal to zero and solve for x

4x + 8 = 0
4 (x + 2) = 0
x = 4, -2

Now put 4 and -2 on a number line

--------------------------------------------------------------
-2 4

Choose three numbers from each region

Lets use -5, 0, 5
Plug in these numbers into the first derivative

f'(-5) = 4(-5) + 8 = - 12

f'(0) = 4(0) + 8 = 8

f'(5) = 4(5) + 8 = 28


decreasing increasing increasing
- + +
-------------------------------------------------------------------------
-2 4

Answer 2

f´(x)= 4x+8=0 so x= -8
sign of f´(x)
----------- -8 +++++++++
decreasing increasing
x<-8 decreasing
x>-8 increasing