If f(2) = 3 and f'(2) = 5, find an equation of the tangent line at the point whe

generals336

generals336

Answered question

2021-09-25

If f(2) = 3 and f'(2) = 5, find an equation of the tangent line at the point where x = 2.

Answer & Explanation

timbalemX

timbalemX

Skilled2021-09-26Added 108 answers

A line that is tangent to f at some point will have the same slope as f at that point.
The slope of f at x = 2 is f'(2), which is given as 5. Thus we need the equation of a line with slope 5 that passes through the point (2,3). In point-slope form:
y-3=5(x-2)
y=5(x-2)+3
y=5x-10+3
y=5x-7
Results:
y=5x-7

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