I need help with this math problem!!!

Question

What is f(x+h) for f(x) = 2x² + 3x - 5

Answer 1

every where you have an x, replace it with x+h

f(x+h)=2(x+h)²+3(x+h)-5

=2(x² + 2xh + h²) +3x +3h -5

= 2x² +4xh +2h² +3x +3h -5

This appears to be part of calculating the derivative, the limit as h goes to zero, for the ratio of [f(x+h)-f(x)]/h=f'(x)

Subtract f(x) from f(x+h) to get 4xh+2h²+3h

then divide by h to get 4x+2h+3

then let h=0

4x+3 is the derivative of 2x²+3x-5

Later you'll learn an easier short cut way to find the derivative,