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What is the equation of the tangent line that passes through the point (-2,10) for the following function?

What is the equation of the tangent line that passes through the point (-2,10) for-example-1
User Mafor
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Given

What is the equation of the tangent line that passes through the point (-2,10) for the following function

Solution


\begin{gathered} f(x)=-2x^2-5x+8 \\ \text{differentiate} \\ -4x-5 \\ \text{substitute x=-2} \\ -4(-2)-5 \\ 8-5=3 \\ \\ we\text{ have y=3x+b} \\ \text{when x=-2} \\ \text{and y=10} \\ 10=3(-2)+b \\ 10=-6+b \\ b=10+6 \\ b=16 \\ \therefore y=3x+16 \end{gathered}

The final answer


y=3x+16

What is the equation of the tangent line that passes through the point (-2,10) for-example-1
User Jemmy
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