It's FALSE that, if f: RR is twice differentiable at no: (a) f' (mo) = 0 and f" (ro) ≤0 ⇒ xo is a local maximum point of f (b) f'(x) = 0 and f" (no) > ⇒ xo is a local minimum point of f (c) then f is differentiable in a neighbourhood of no (d) then f(x) = f(no) + f'(no) (n−no) + ±f" (no) (n-x0)² + 0 ((n-2)²) as 2→xo (e) f'(x) = 0 ⇒ xo isn't a local extremum point of

It's FALSE that, if f: RR is twice differentiable at no: (a) f' (mo) = 0 and f" (ro) ≤0 ⇒ xo is a local maximum point of f (b) f'(x) = 0 and f" (no) > ⇒ xo is a local minimum point of f (c) then f is differentiable in a neighbourhood of no (d) then f(x) = f(no) + f'(no) (n−no) + ±f" (no) (n-x0)² + 0 ((n-2)²) as 2→xo (e) f'(x) = 0 ⇒ xo isn't a local extremum point of

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

See similar textbooks

Similar questions

If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?
3. Is there a twice differentiable function f : R² → R whose best quadratic approximation at the point (1,0) is f itself? Explain your an- swer.
Show that the function f(z)= Im(z) is nowhere differentiable.
4. Find the analytic function whose real part is u(x, y) = e* cos y. 5. Find the analytic function whose real part is u(x, y) = e-y sin x.
Q3) Let f(z) = 4y + x³ + i(y3 – 4x) a) Determine where the function f(z) is differentiable b) Determine the domain in which f(z) is analytic
Let f be a twice differentiable function on an open interval (a, b). Which statements regarding the second derivative and concavity are true? If f" (c) is positive, then the graph of f has a local maximum at x = c. If f is increasing, then the graph of f is concave down. The graph of f is concave up if f" is positive on (a, b). The graph of f has a local minimum at x = c if ƒ" (c) = 0. The concavity of a graph changes at an inflection point.
Check that the equation x³ + y³ + z³ = x + y + z implicitly defines at least one differentiable function z = z (x, y). Express az/ ax and az/ay in terms of x, y, z
Find the maximum value of of Iƒ" (x) [0,2] f(x)=√1+x² HINT: Much like the previous question except that you are focussing only on the max. Input your function as surd((1+x^2),2); Let your second derivative function equal abs(df2); assuming that df2 is the second derivative. Substitute your endpoints 0 and 2 into your absolute value second derivative function. Find third derivative and solve it for x. Substitute the result obtain into your second derivative absolute value function. Compare all y-values obtained for maximum value. 5) on the indicated interval. 6) Without the aid of a graph, find the absolute maximum and minimum values of the function
2C
Show that f(x) = 2a + 3b is continuous, where a and b are constants
Suppose f is a differentiable function such that f(-2) = 3 and f(5) = 17. Then there must be a point c in the interval (-2,5) for which f'(c) = %3D
4. a. Let f(x) = ax²+3x+y be a quadratic function with a, 3,7 € R. Consider the closed interval [a, b] which has midpoint c = a+b. Prove that the slope of the secant line join- ing (a, f(a)) to (b, f(b)) is equal to the slope of the tangent line to f(x) at the point c. b. What you did in part a. was prove that the midpoint c is the same as the point c specified in the Mean Value Theorem applied to f(x) on the interval [a, b]. This is a special property of quadratic functions. It does not work in general. Find a counter example to demonstrate this. Your counterexample should specify both the function and the interval you are looking at.