If h(1) = 2 and h′(1) = 3, find an equation of the line tangen...

Question

If h(1) = 2 and h′(1) = 3, find an equation of the line tangent to the graph of h at x = 1.

Accepted Answer

Welcome back everyone to another video. For a certain function F, it is known that F of 3 is equal to -1 and F 3 is equal to 4. Determine the equation of the tangent line to functions graph at X equals 3. We're given 4 answer choices A says Y equals -4 x + 11 B 4 x minus 11. C4 x minus 13, and D4X plus 13. So let's recall that the equation of the tangent line is equal toy equals F at the point of interest X not. Multiplied by x minus the point of interest x0 plus the value of the function at that point F of X and in this case we're looking at point X equals 3 so we're looking for Y equals F at. 3 multiplied by x minus 3 plus F at 0.3, right? So we know that F at 3 is equal to 4, and also F of 3 is equal to -1. So Y equals 4, right? That's our slope, multiplied by X minus 3. Plus F of 3 which is -1. And now if we distribute, we're going to get 4 x minus 12. 1 simplifying Y equals 4 x minus 13. Which essentially corresponds to the answer choice. See, let's label it as our final answer, and thank you for watching.

If h(1) = 2 and h′(1) = 3, find an equation of the line tangent to the graph of h at x = 1.

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