find derivative using definition of derivative

Question

 

 

             Use the defnition of a derivative to find the derivative of y=1.5x^2-x+3.7             

Answer 1

Let f(x) = y = 1.5x² - x + 3.7

f(x + h) = 1.5(x + h)² - (x + h) + 3.7 = 1.5(x²+2xh+h²)-(x + h) + 3.7

f(x + h) = 1.5x²+3xh+1.5h²-x - h + 3.7

Fundamental theorem of differentiation:

Take out common term h.

Therefore y' = 3x - 1.