Calculus Questions

The function is continuous and differentiable on the closed interval [3,7]. The table above gives selected values of f on this interval. Which of the following statements must be true?I. The minimum value of f on [3,7] is 12II. There exists c, for 3<c<7, such that f'(c)=0III. f'(x)>0 for 5<x<7

Let g be a twice-differentiable, increasing function of t. If g(0)=20 and g(10)=220, which of the following must be true on the interval 0<t<10?

The function f given by f(x)=3x^5-4x^3-3x has a relative maximum at x=

x,y:0,21,32,43,34,2The function f is continuous and differentiable on the closed interval [0,4]. The table above gives selected values of f on this interval. Which of the following statements must be true?

Let f be a twice-differentiable function. Values of f', the derivative of f, at selected values of x are given in the table above. Which of the following statements must be true?

Is the b value inside or outside the parentheses?

x,y: -1,-300,-23,105,18The table above gives selected values for a twice-differentiable function f. Which of the following must be true?

Let f be a function given by f(x)=kx/(x^2+1), where k is a constant. For what values of k, if any, is f strictly decreasing on the interval (-1,1)?

A portion of the graph of a differentiable function is shown above. If the value c=3 satisfies the conclusion of the Mean Value Theorem applied to f on the open interval -2<x<8, what is the slope of the line tangent to the graph of f at on x=3?

The sides and diagonal of a rectangle above are strictly increasing with time. At the instant when x=4 and y=3, and dx/dt=dz/dt and dy/dt=kdz/dt. What is the value of k at that instant?

The table above gives the values of the continuous function f at selected values of x. If f has exactly two critical points on the open interval (10,14), which of the following must be true?

If the base b of a triangle is increasing at a rate of 3 inches per minute while its height h is decreasing at a rate of 3 inches per minute, which of the following must be true about the area A of the triangle?

The maximum acceleration attained on the interval 0<t<3 by the particle whose velocity is given by v(t)=t^3-3t^2+12t+4 is

The volume of a sphere is decreasing at a constant rate of 3 cubic centimeter per second. At the instant when the radius of the sphere is decreasing at a rate of 0.25 centimeter per second, what is the radius of the sphere (The volume V of a sphere with the radius r is V4/3pier^3

If y=xy+x^2+1, then when x=1, dy/dx is

The radius of a circle is decreasing at a constant rate of 0.1 centimeter per second. In terms of circumference C, what is the rate of change of the area of the circle, in square centimeters per second?

The volume of a certain cone for which the sum of its radius, r, and height is constant is given by V=1/3pier^2(10-r). The rate of change of the radius of the cone with respect to time is 6. In terms of r, what is the rate of change of the volume of the cone with respect to time?

The graph of f(x) = x^2 is shown.Use the parabola tool to graph g(x).g(x) = (x + 2)^2 − 1Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

The radius of a circle is increasing at a nonzero rate, and at a certain instant, the rate of increase in the area of the circle is numerically equal to the rate of increase in its circumference. At this instant, the radius of the circle is

Which answer describes the transformation of f(x)= x^2 − 1 to g(x) =(x+4)^2 − 1 ?