Estimate the slope of y = x^2+3x at x = 3. Justify your answer.

Question

 This is a calculus question that I need help on.

Answer 1

The slope of the curve at a given point is the derivative evaluated at that point.  

 

y = x² + 3x

 

y' = 2x + 3

 

When x = 3, y' = 9 = slope of curve when x=3 

Answer 2

If you want the exact slope, the slope of the tangent line is dy/dx evaluated at x = 3.

 

y = x² + 3x

 

dy/dx = 2x + 3

 

At x = 3,

 

dy/dx = 2(3) + 3 = 9

 

The slope at (3, f(3)) is 9.

Answer 3

f(2) = 10

f(4) = 28

m = 18 / 2

m = 9