Calc BC First Week of HW Test

Find the slope of the tangent line to the graph of the function at the given point.

f(x) = -3x^2 - 1, (-8, -25)

• -6

• 48

• -48

• -14

Use the product rule to differentiate.

f(x)=x^3 sin x

• x^3 sin x + 3x^2 cos x

• x^3 sin x - 3x^2 cos x

• x^3 cos x - 3x^2 sin x

• x^3 cos x + 3x^2 sin x

Use the quotient rule to differentiate.

f(x) = (4x)/(x^3+5)

• (4(x^3+5) - 4x(3x^2)) / (x^3+5)^2

• (4(x^3+5) + 4x(3x^2)) / (x^3+5)^2

• ( 4x(3x^2) - 4(x^3+5)) / (x^3+5)^2

• ( 4x(3x^2) - 4(x^3+5)) / (x^3+5)

Find the limit as x approaches infinity of

(-4x-2)/(-6x+1)

• -2/3

• 3/2

• 2/3

• -1/2

Find the derivative of the function.

f(x)= -4x^3 + 2 cos x

• -12x^2 - 2 cos x

• -12x^2 - 2 sin x

• -4x^2 + 2 sin x

• -8x^2 - 2 cos x

Find dy/dx by implicit differentiation.

x^2 + y^2 = 25

• -y/x

• -x/y

• x/y

• y/x

Find the derivative of the function.

y = ln (sqrt(x^2-25)

• x/(x^2-25)

• 1/(x^2-25)

• x/sqrt(x^2-25)

• 2x/sqrt(x^2-25)

Identify the open intervals where the function f(x)=-6x^2 - x +2 is increasing or decreasing.

inf=infinity

• increasing (-inf, inf)

• decreasing (-inf, inf)

• decreasing (-inf, -1/12) increasing (-1/12, inf)

• increasing (-inf, -1/12) decreasing (-1/12, inf)

Find the derivative

f(x)=5x^3 + 6x^2 +12

• 15x^2 + 6x

• 15x^2 + 12x

• 15x^2 + 12x +1

• 8x^2 + 6x + 1

Find the indefinite integral of x^2/(20x^3 + 2)

• ln |20x^3 + 2|+C

• x^3/(20x^4 + 2) + C

• (1/60) ln |20x^3 + 2|+C

• (20x^3 + 20)+C