find the slope of the functions graph at the given point. then find an equation for the line tangent to the…

find the slope of the functions graph at the given point. then find an equation for the line tangent to the graph \n\n$f(x)=4x^{2}+3x,(-2,10)$\n\nthe slope of the functions graph at $(-2,10)$ is \n(simplify your answer.)

find the slope of the functions graph at the given point. then find an equation for the line tangent to the graph \n\n$f(x)=4x^{2}+3x,(-2,10)$\n\nthe slope of the functions graph at $(-2,10)$ is \n(simplify your answer.)

Answer

Explanation:

Step1: Differentiate the function

Using the power rule ((x^n)^\prime = nx^{n - 1}), for (f(x)=4x^{2}+3x), we have (f^\prime(x)=(4x^{2})^\prime+(3x)^\prime). (f^\prime(x)=4\times2x+3) (f^\prime(x)=8x + 3)

Step2: Substitute (x=-2) into the derivative

To find the slope at (x =-2), substitute (x=-2) into (f^\prime(x)). (f^\prime(-2)=8\times(-2)+3) (f^\prime(-2)=-16 + 3) (f^\prime(-2)=-13)

Answer:

(-13)