Find f'(x) of f(x)=x2-15+10by using definition

Answer 1

you mean f(x) = x^2-15x+10, or else the constants will

combine to make f(x) = x^2-5 and I have never seen the

functions written like that...

f(x+h) = (x+h)^2 - 15(x+h) + 10

= x^2 + 2xh + h^2 - 15x - 15h + 10

= x^2 -15x + 10 + 2xh + h^2 - 15h

the numerator of the difference quotient is:

f(x+h) - f(x) = 2xh + h^2 - 15h

dividing by h:

2x + h - 15

finally, the limit as h-->0:

2x-15

which agrees with the derivative via power rule