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+1 vote
Finding the derivative at an unspecified point

use this formula to solve the problem : f '(x)= lim f(x+h)-f(x)/h
h->0
problem : f(x)=x^2+3x-7

please show the steps
asked Feb 21, 2013 in CALCULUS by angel12 Scholar

1 Answer

+1 vote

f(x) = x2 + 3x - 7

f(x + h) = (x + h)2 + 3(x + h) - 7

f(x + h) = x2 + h2 + 2xh + 3x + 3h - 7

f(x + h) - f(x) = [x2 + h2 + 2xh + 3x + 3h - 7] - [x2 + 3x - 7]

f(x + h) - f(x) = x2 + h2 + 2xh + 3x + 3h - 7 - x2 - 3x + 7

f(x + h) - f(x) = h2 + 2xh + 3h

Take out common term h.

f(x + h) - f(x) = h(h + 2x + 3)

Fundamental theorem of differentiation formula:

image

But f(x + h) - f(x) = h(h + 2x + 3)

image

image

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answered Feb 21, 2013 by britally Apprentice

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