Find the Tangent Line at x=4 f(x)=x^2+5x , x=4

Problem

ƒ(x)=x2+5*x,x=4

Solution

1. Find the y-coordinate by evaluating the function at x=4

ƒ(4)=(4)2+5*(4)

ƒ(4)=16+20

ƒ(4)=36

2. Find the derivative of the function to determine the slope formula.

(d(x2)+5*x)/d(x)=2*x+5

3. Calculate the slope m by evaluating the derivative at x=4

m=2*(4)+5

m=8+5

m=13

4. Apply the point-slope formula y−(y_1)=m*(x−(x_1)) using the point (4,36) and slope m=13

y−36=13*(x−4)

5. Simplify the equation into slope-intercept form.

y−36=13*x−52

y=13*x−52+36

y=13*x−16

Final Answer

y=13*x−16

Want more problems? Check here!