Curve Sketching Techniques with Derivatives

Which of the following shapes is concave down?

• A circle

• A U-shape opening upwards

• A U-shape opening downwards

• A straight line

What is the sign of the second derivative for a concave upward shape?

• Undefined

• Zero

• Positive

• Negative

If a function is increasing, what is the sign of its first derivative?

• Positive

• Negative

• Zero

• Undefined

What are the x-intercepts of the polynomial function f(x) = x^3 + 6x^2 + 9x?

• 1 and -1

• 3 and -3

• 0 and 3

• 0 and -3

What is the first derivative of the function f(x) = x^3 + 6x^2 + 9x?

• x^2 + 6x + 9

• 3x^2 + 12x + 9

• 3x^2 + 9x + 6

• 3x^2 + 6x + 9

What is the critical point of the function f(x) = x^3 + 6x^2 + 9x?

• -3 and -1

• 0 and -3

• 0 and 3

• 3 and -1

What is the second derivative of the function f(x) = x^3 + 6x^2 + 9x?

• 6x + 12

• 6x + 9

• 3x + 9

• 3x + 12

What is the y-value of the function f(x) = x^3 + 6x^2 + 9x at x = -1?

• -4

• 4

• -2

• 0

What are the x-intercepts of the polynomial function y = 3x^4 + 4x^3?

• 3 and -4/3

• 3 and 4/3

• 0 and 4/3

• 0 and -4/3

What is the first derivative of the function y = 3x^4 + 4x^3?

• 3x^3 + 4x^2

• 12x^3 + 12x^2

• 3x^3 + 12x^2

• 12x^3 + 4x^2