If the tangent line to the curve #y = f(x)# at the point where #a = 2# is #y = 4x-5# , find #f(2)# and #f'(2)#? I know #f(2) = 3# but how do I find #f'(2)#?

Question

My textbook says #f'(2) = 4# but how exactly?

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Answer 1 · 2017-04-21T09:44:57

# f'(2)=4#

The tangent to the curve #y=f(x)# is

# y=4x-5 #

Comparing with #y=mx+c # we see that #m=4# so the gradient is #4#, and the gradient is also #f'(2)#