question 9 (3 points)\ndetermine the equation of the tangent to ( f(x)=x^{2}+x ) at the point (1…

question 9 (3 points)\ndetermine the equation of the tangent to ( f(x)=x^{2}+x ) at the point (1, 2).\n*please insert and image of your solution below.*

question 9 (3 points)\ndetermine the equation of the tangent to ( f(x)=x^{2}+x ) at the point (1, 2).\n*please insert and image of your solution below.*

Answer

Explanation:

Step1: Find the derivative of the function

The derivative of (f(x)=x^{2}+x) using the power rule ((x^n)^\prime = nx^{n - 1}). (f^\prime(x)=(x^{2}+x)^\prime=(x^{2})^\prime+(x)^\prime = 2x + 1)

Step2: Evaluate the derivative at (x = 1)

Substitute (x = 1) into (f^\prime(x)) to get the slope (m) of the tangent line. (m=f^\prime(1)=2(1)+1=3)

Step3: Use the point - slope form of a line

The point - slope form is (y - y_1=m(x - x_1)), where ((x_1,y_1)=(1,2)) and (m = 3). (y - 2=3(x - 1))

Step4: Simplify the equation

Expand and simplify (y - 2=3x-3). (y=3x-3 + 2) (y=3x-1)

Answer:

The equation of the tangent line is (y = 3x-1)