Consider the curve y=x2+3x+5. (a) find the slope of the secant line to the curve through the points p=(4,33) and q=(4+h,(4+h)2+3(4+h)+5). 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= .

a) The slope of the secant line is 11 + h

b) The slope of the curve at P is 11

c) The equation of the tangent line at P is y = 11x - 11

Step-by-step explanation:

y=x²+3x+5

(a) Find the slope of the secant line to the curve through the points P=(4,33) and Q=(4+h,(4+h)²+3(4+h)+5)

(4+h)²+3(4+h)+5 = 16 + 8h + h² + 12 + 3h + 5 = 33 + 11h + h²

slope (m) = yq - yp/xq - xp → m = 33 + 11h + h² - 33/4 + h - 4

m = 11h + h²/h = h(11+h)/h = 11 + h

The slope of the secant line is 11 + h

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

As P (4,33) = (4+0, 33+0) at P h is 0, so the slope at P is 11 + 0 = 11

The slope of the curve at P is 11

(c) Write an equation of the tangent line to the curve at P.

y - yp = m(x - xp) → y - 33 = 11(x - 4) → y - 33 = 11x - 44 → y = 11x - 11

The equation of the tangent line at P is y = 11x - 11

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.

the answer is c just got it on ed

step-by-step explanation: