Question

Given that 𝑓(−1)=3and 𝑓′(−1)=2,find an equation for the tangent line to the graph of 𝑦=𝑓(𝑥)at 𝑥=−1

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Answer 1

We know that the derivative indicates the slope of the tangent line:

$$m=f'(-1)=2$$

Therefore, the tangent line requested is the line that passes through the point $(-1,3)$ and has $m=2$ as slope:

$$y-3=2(x+1)\Rightarrow y=2x+5$$