ists for all z € I (but f' need not itself be continuous). Suppose further at f'(a) < f'(b). Prove for any y with f'(a) < y < f'(b) that there is me ce I such that f'(c) = y.

Q: These are true or false questions

A: 3) If f(x) is differentiable at any point x=a, then it must be continuous at x=a So the given…

Q: 1. Express the followings in the form of x + iy where r, y E R.(choose one.) (a) 금+ 부 (b) ( + ) ( –…

A: Rationalise  all the term and calculate to get the final answer.   Actually as per the barteleby…

Q: Suppose  f ( 200 , 300 ) = 1000and ∂ f ∂ x ( 200 , 300 ) = 12 and ∂ f ∂ y ( 200 , 300 ) = 10.…

A: Given, f(200,300)=1000 ∂f∂x(200,300)=12∂f∂y(200,300)=10

Q: Let f(x) = (a) f(1) = (b) f'(6) = 2x³ - 5x² x2 Evaluate f'(x) at the following points:

A: f(x)=2x3-5x2x23xba=xbad dx(x)m=mxm-1

Q: Draw a graph for following f' > 0 on (-∞,1) and f"l > 0 on (-∞, 1) U (1, ∞).

A:

Q: Suppose f is continuous, positive, decreasing, and concave up on the interval [5, 15]. Compare each…

A: 1) &gt; left sum will be greater than right because function is decreasing 2)  &lt; because…

Q: If f is concave up, then f' is (choose one): (a) increasing. (b) decreasing.

A:

Q: Suppose you know that the function f is decreasing and concave down on t interval [2, 7]. which of…

A: If the first derivative of a function is negative then the function is decreasing and vice versa.…

Q: Let f(x, y) = e²x* %3D Evaluate f(3, 5)

A: Given :   f ( x, y) = exy x4   point ( 3,5)

Q: Suppose f" () > 0 on some interval (a, b). Check all of the following statements that must be true.…

A: Step 1: Let write the given .We are given that f"(x)&gt;0 on some interval (a,b). Step 2: Let write…

Q: Suppose that a function h satisfies −x^2 ≤ h(x) ≤ x^2 for all x. Prove that h is differentiable at x…

A:

Q: Please just do 1(b)

A: To compute the required value , by definite integral

Q: Suppose that S(m)3(4#-4)*(32+ 1). Find f'(#), and then evaluate f' at # = 1 and # = -1 (1)= 1(-1)=

A:

Q: if f'(a) exists, then f is continuous at x = a. True False

A: Function f differentiable at x=a

Q: Given the graph of ƒ' (x) below, where the Dom f (x) = (-∞, ∞) . Find ALL interval(s) for which f""…

A:

Q: The graph of the function f'(x) of a continuous function f is shown. On what intervals is f concave…

A: It is given that,the graph of the function f'(x) of a continuous function f.  We have to find…