Applications of Derivatives
Math ⇒ Calculus
Applications of Derivatives starts at 11 and continues till grade 12.
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See sample questions for grade 11
A function has a critical point at x = 2. If f''(2) = 0, what can you conclude about the nature of the critical point?
If f'(x) changes from positive to negative at x = c, what does this indicate about f(x) at x = c?
If the second derivative of a function at x = a is positive, what does this indicate about the function at x = a?
If the tangent to the curve y = f(x) at x = a is horizontal, what is the value of f'(a)?
A ball is thrown upwards and its height at time t seconds is given by h(t) = -5t² + 20t + 2. Find the time when the ball reaches its maximum height.
A box with a square base and open top must have a volume of 32 cubic units. What is the minimum surface area?
A rectangle has a perimeter of 20 units. What is the maximum possible area of the rectangle?
If the position of a particle is given by s(t) = t³ - 6t² + 9t, find the time when the particle changes direction.
A function f(x) has a local minimum at x = 1. Which of the following must be true? (1) f'(1) = 0 (2) f''(1) > 0 (3) f'(1) > 0 (4) Both (1) and (2)
A function f(x) is concave down on an interval if: (1) f'(x) < 0 (2) f''(x) < 0 (3) f'(x) > 0 (4) f''(x) > 0
A function f(x) is decreasing on an interval if: (1) f'(x) > 0 (2) f'(x) < 0 (3) f''(x) > 0 (4) f''(x) < 0
The maximum or minimum value of a function on a closed interval can occur at: (1) Critical points only (2) Endpoints only (3) Both critical points and endpoints (4) Neither
A function is increasing when its first derivative is ________.
If the derivative of a function is zero everywhere, the function is a ________ function.
The derivative of a function at a point is zero. This point is called a ________ point.
The point where the concavity of a function changes is called a(n) ________ point.
True or False: If the first derivative of a function at a point is zero, the function must have a maximum or minimum at that point.
True or False: The derivative of a function at a point gives the slope of the tangent at that point.
True or False: The first derivative test can be used to determine whether a critical point is a maximum or minimum.
True or False: The maximum or minimum value of a function on a closed interval always occurs at a critical point.
