Domain of f is R – 0 f(x) = 0 if x = 1. lim→+∞ f(x) = 0 and lim,→0+ f(x) = lim,→0- ƒ(x) = -∞ %3D f'(x) = 0 if x = 2 and f'(x) does not exist at x = 0 and f(2) = 9/2. f'(x) < 0 on (-0, 0) U (2, ∞0) and f'(x) > 0 on (0, 2) f"(x) = 0 if x = 3 and f"(x) does not exist at x = 0 and f(3) = 4. f"(x) < 0 on (–∞, 0) U (0, 3) and f"(x) > 0 on (3, ∞) Complete the sign table: f'(x) | f"(x) f(x) Write the inflection point(s), critical point(s) and the local extrama of f, if exist. Write the vertical, horizontal asymptotes of f, if exist.

Q: etch the graph of a function that satisfies all of the given conditions. f'(5) = 0, f'(x) 0 when x…

A: We will find the required graph.

Q: What is the appropriate form of the derivative of g(x)= -x³ – 7? g' (x) = limaz→a (-z*–7)–{(a) Az-a…

A: Given function, g(x)=-x3-7

Q: x - x +2 4. If flx) =x + 7 find f'(x) . (5x - 1) (3x²) (A) (x' + 7)(5x - 1) – (x° – x + 2)(3x²) (B)…

A: The given function is  f(x) = x5-x+2x3+7

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² and suppose that Find F'(8) and G'(8). = F'(8) = G'(8) = ƒ(8)…

A:

Q: the line 3x+ y=l is the tangent line for the graph of y= f(x) at x=1, then f'(1)= 1 (C) 1 (D) 3 A) 3…

A: The slope of the line y=mx+c is m. The slope is equal to the derivative of y i.e., f'y=m

Q: If f(x) = (x² +2) e², what is f'(x)?

A:

Q: The graph of y = f(x) is given below. Th 0 2 Which statement is true? O f'(5) < f'(-2) < f'(1) O…

A:

Q: Find the derivative of the function f(x) = 3x2- 13x 25 by definition of derivatives f(x + h) - f(x)…

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: Find a function ƒ(x) such that ƒ'(x) = −8x² + 1 and ƒ(0) = 1 ƒ(x) = |

A: f'(x)=-8x2+1f(0)=1∫xndx=xn+1n+1+c

Q: A Function f(x) is defined for all xr>0, and satisfies f(x2) = x3 for all x > 0.Show that f is…

A:

Q: Find the value of the derivative at each relative extremum shown

A: We have to find derivative at each relative extremum as in shown in figure.

Q: Q14: : Find intervals where function f is concave up and concave down and find the inflection…

A: Consider the function  f(x)=xex

Q: Giren f(e) = 2x+1 and g(4) = x*+ 2x-1, in (- () Then valute he difcene hen x=2.

A:

Q: Let f' (x) 0 for all x with -o∞ f(c) More information is needed.

A: Given  Let f'x&lt;0 and f''x&gt;0 for all x with -∞&lt;x&lt;∞ Let a,fa and  c,fc be two points on…

Q: 3X + 3AX + 2 f'(x) = lim Ax→0 Ax

A: We have to find the value of f'(x).

Q: f(x) = sec x As x = π-/2, f(x) =  As x = π+/2, f(x) =

A:

Q: -5 -4 -3 -2 -1 As x → 1- As x → 1+ I f'(1) = > 10 4 3 2 1 3 5 1 2 (b) Use the definition of a…

A:

Q: If f"(x) = x³ – 2 x* + x³ + 2, then f has inflection points at

A:

Q: Let f(x) be a function with second derivative of f"(x) = -(5x +11)?(x – 2) Determine the local…

A: When a function's at critical point x , and the second derivative at x is: less than 0, it is a…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.