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The function f that satisfies f'(x) = 3x2 +1, f(2)=5 is Select one: a. f(2)=23+ O...
If f'(x) = (x – 7)(x-1), the function f(x) is increasing on: Select one: O a. (-0,1) O b. (-1,0) O c. (-0,7) O d. (7,00) O e. (-1,7)
help Spt 7. Verify that the function f(x) = Vr+1 satisfies the hypotheses of the Mean Value Theorem on the interval (0,3). Then find all numbers c that satisfy the conclusion of the Mean Value Theorem. pt 8. Find the absolute maximum and absolute minimum values of the function f(x)- In(4r2 +2r+1) on the interval -1,0). Spt 7. Verify that the function f(x) = Vr+1 satisfies the hypotheses of the Mean Value Theorem on the interval (0,3). Then find all...
Let us verify the Mean Value Theorem with the function f(x) = VE on the interval (2,8). Solution. We have f is continuous on (2,8) f is differentiable on (2,8). f'(o) – f(8) – f(2) 8 - 2 We have f'(x) = The only value that satisfies the Mean Value Theorem is
Evaluate f(x) = -x3 + 4x5 - 3x2 + 1 at -1 and -3 to determine if the Intermediate Value Theorem guarantees that a zero exists between the two values. a) f(-1) = b) f(-3) = c) Does the Intermediate Value Theorem guarantee that a zero exists between -1 and -3?
Show that the function flx)- x+8x+5 has exactly one zero in the interval [-1, 01. Which theorem can be used to determine whether a function f(x) has any zeros a given interval? O A. Extreme value theorem O B. Intermediate value theorem OC. Rolle's Theorem O D. Mean value theorem apply this theorem, evaluate the function fix)x +8x+5 teach endpoint of the interval [-1, 01 f-1)(Simplify your answer.) f(0) (Simplify your answer.) According to the intermediate value theorem, f(x) x...
Theorem 2.3.1 If f is continuous on an open rectangle (a) that contains (xo yo) then the initial value problem f(a, y), y(o)yo has at least one solution on some open subinterval of (a, b) that contains ro (b) If both fand fy are continuous on R then (2.3.1) has a unique solution on some open subinterval of (a, b) that contains ro. In Exercises 1-13 find all (xo, Vo) for which Theorem 2.3.1 implies that the initial value problem...
2 12, (a) Find the function f that satisfies the given initial condition. (5 points) f' (x) = x3/2 +-5/2 f(1)-4 : [5 points) 2 12, (a) Find the function f that satisfies the given initial condition. (5 points) f' (x) = x3/2 +-5/2 f(1)-4 : [5 points)
My Notes 5. -'2 points SCalcET8 1.2.505.XP. (a) Graph the function fix) = x + 5/x and the secant line that passes through the points (1·6) and (10. 1 0.5) In the viewing rectangle [D, 1 2jby [D, 1 2]. 12 12 10 10 12 12 12 12 10 10 1 12 (bFind the numher c that satisfies the concluslon of the Man ale Theorem for this function fand the Interva [, 1D Need Help Read ItWatch It Talk to...
Consider the following. f(x) = 1 4 x4 + 1 2 x3 − 3x2 + 4 Find f '(x). f '(x) = x3+ 3x2 2−6x Find f ''(x). f ''(x) = 3x2+3x−6 Find the x-values of the possible points of inflection. (Enter your answers as a comma-separated list.) x = Determine the intervals on which the function is concave up. (Enter your answer using interval notation.) Determine the intervals on which the function is concave down. (Enter your answer using...
1-8 please 1. Find the value c that satisfies Rolle's Theorem for f(x) = cos x on A / B./2 C. D. E. 0 F. None of the above 311/4 2. The function f is graphed below. Give the number of values that satisfy the mean value theorem on the interval (-6,6). A. 0 B. 1 C. 2 D. 3 E. 4 F. None of these Page 1 of 5 1. The graph off) is shown. Find the value(s) where)...