The line tangent to the graph of function f at the point (8,1) intersects the y-axis at y=3. How do you find f'(8)?

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The line tangent to the graph of function f at the point (8,1) intersects the y-axis at y=3. How do you find f&#039;(8)?

kuwebux78 · Accepted Answer

You have choices for how to write the equation of the tangent line.Point Slope Form solutionThe tangent line contains point (8,1) and has slope f&#039;(8), so its equation isy-1=f&#039;(8)(x-8)The line contains (0,3), so we get3-1=f&#039;(8)(0-8) which leads tof′(8)=−14Slope-Intercept Form solutionThe tangent line has slope f&#039;(8) and y-intercept 3, so the equation of the tangent line isy=f&#039;(8)x+3We know that the point (8,1) is on the line, so we get1=f&#039;(8)*(8)+3.This leads to f′(8)=−14

indomanihle · Accepted Answer

Explanation:We know that the tangent line at x=8 passes through the points (8,1) and (0,3).The slope of the line that passes through these points isf′(8)=3−10−8=2−8=−14.

The line tangent to the graph of function f at

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