Consider the curve

(a) Find the slope of the secant line to the curve through the points $P = (4, 35)$ and $Q = (4+h, \left(4+h\right)^{2}+3\!\left(4+h\right)+7)$.
The slope of the secant line is .

(b) Use your answer from part (a) to find the slope of the curve at the point $P$.
The slope of the curve at $P$ is .

(c) Write an equation of the tangent line to the curve at $P$.
The equation of the tangent line at $P$ is $y =$ .

Your overall score for this problem is