Use the limit definition of the derivative to find the slope of the tangent line to the curve f ( x ) = 6 x − 3 at x = − 3

Question

Use the limit definition of the derivative to find the slope of the tangent line to the curve   f ( x ) = 6 x − 3   at   x = − 3

Patrick B. · Accepted Answer

f(x+h) = 6(x+h) -3 = 6x+6h-3

f(x+h)-f(x) = 6x+6h-3 -(6x-3)

= 6h

f(x+h)-f(x) all over h

= 6h/h = 6

limit as h->0 is 6

the derivative is 6, which agrees with power rule

the slope of the tangent line is 6

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