What is the equation of the line tangent to #f(x)=x ^3 # at #x=1#?

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Answer 1 · 2016-03-11T08:14:09

#y = 3x - 2#

#f(x) = x^3#
#f'(x) = 3x^2#

Equation of a straight line with slope m and intercept on the y-axis c is given by:

#y = mx + c#

In this question we are asked to find the line tangent to f(x) at x=1

Slope of f(x) at #x = 1# is #f' (1) = 3 .1^2 = 3 -> m = 3#
Since #f(1) = 1# we know that the tangent line passes through the point (1,1)

Hence substituting for x, y and m in the equation above:

#1 = 3. 1 + c#
#c = -2#

The tangent line is therefore #y = 3x - 2#