Science:Math Exam Resources/Courses/MATH 180/December 2017/Question 03 (b)/Solution 1

We use Hint 1 with ${\textstyle a=5}$. So the equation of the tangent line of ${\textstyle y=f(x)}$ at ${\textstyle x=5}$ is

$$y=f(5)+f'(5)(x-5).$$

We are given that ${\textstyle f(5)=-8}$ and ${\textstyle f'(5)=4}$. Hence, the equation is of the tangent line becomes

$$y=-8+4(x-5).$$

By Hint 2, we need to find the value of ${\textstyle y}$ when ${\textstyle x=0}$. So we put ${\textstyle x=0}$ to find

$$y=-8+4(0-5)=-8-20=-28.$$

Therefore, the ${\textstyle y}$-intercept of the tangent line is ${\textstyle -28}$.

Answer: The ${\textstyle y}$-intercept of the tangent line is ${\textstyle {\color {blue}-28}}$.