Given
What is the equation of the tangent line that passes through the point (-2,10) for the following function
Solution
[tex]\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}[/tex]
The final answer
[tex]y=3x+16[/tex]
