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

well the 1 and -1 are always after the 0 and the 0 is inthe middle. s thats what i would guess. but i dont know what a slope of 2 is sorry

step-by-step explanation:

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1