6. Let f be the function given by f(x) In x for all x > 0. The derivative of f is given by f'(x) = %3D (a) Write an equation for the line tangent to the graph of f at x = e". (b) Find the x-coordinate of the critical point of f. Determine whether this point is a relative minimum, a relative maximum, or neither for the function f. Justify your answer. (c) The graph of the function f has exactly one point of inflection. Find the x-coordinate of this point. (d) Find lim f(x).

Q: 2. In the figure above, f', the derivative of function f, is shown. f is a twice differentiable…

A: We need to find properties of f from f' graph.

Q: Consider the function h(x) = 1/5 x^5 − 1/3 x^3 + 2. a)  Using derivatives, find the interval(s)…

A:

Q: The temperature in degrees Celsius (C) in Toronto starting on March 1** can be represented by the…

A:

Q: 75 2. Let f(x) = 2+ 3x² on the interval 15z5 50. (a) Use the approximation formula to estimate the…

A: (a) The approximate derivative of the function is given by f'(1+h)≈f(1+h)-f(h)h, where 1≤h≤49 and is…

Q: 9. Use the definition of derivative to find the derivative of f(x) = x² – 3x.

A: We need to evaluate the derivative of the function f(x) using definition of the following function…

Q: For the function y = h(x) whose graph is shown, find the values of x such that the derivative is…

A: For the given function: y=hx The graph shown is:

Q: Exercise 5: For the following graphs, sketch a graph of the derivative (i.e., you are given f;…

A: Consider the given curve of f(x).

Q: Let f be a function defined on the closed interval -4sxs4. The graph of f', the derivative of f, is…

A: Let's find.

Q: The graph of f(x) is given below. On what interval(s) is the value of the derivative f'(x) negative?…

A: Given : The graph of the function f(x). To find : On what interval(s) is the the value of the…

Q: 6x erivative of f(x) equal to zero, calculate x*: f'(x*) = 0. Using the second derivative ther x* is…

A:

Q: 2. For the function, f(x), below, state the intervals of increase and decrease, the x-coordinates of…

A: The interval of increase: From the graph of the function, we can see that the function is increasing…

Q: what is a and b please?

A: Use chain rule to find the h ' (x) and g ' (x).

Q: ph represents the derivative function f'(x) of a function f(x). rval of increase and decrease of the…

A:

Q: Find the x value(s) for any relative extrema. Use the Second Derivative Test to determine if this 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.