8) (a) The diagram is a sketch of y = f(x). y 1 Draw separate one third page sketches of the graphs of the following: (i) f(x) (ii) y = f(x[) (iii) (x)f* = A

Q: d) A function with no absolute extrema but with a local minimum of -5 at x = 4 and a local maximum…

A: Follow the procedure given below.

Q: 6. Find the absolute minimum and maximum of the function f(x) = x° – 12x+5 interval [0, 3]. on the

A: The function is given by fx = x3-12x+5 To evaluate : The absolute maximum and the absolute minimum…

Q: 2. Find the absolute maximum and absolute minimum value of f(x) = 6x – x on [1, 7].

A: Given function fx=6x-x2 To find the absolute maximum and minimum first find critical values.…

Q: Find the local and/or absolute maxima for the functions of the specified domain. Y= 1/(x-x^2) over…

A: Here we have to use the concept of derivatives. Here we use second derivatives test for finding…

Q: 6. Sketch an even continuous function with all of the following features: • Absolute maximum at 6 •…

A: We can solve this using given information As we know the even function is nothing but symmetric…

Q: 1-x3 , х0 . Sketch the graph.

A:

Q: 11.  Let h(x) = x^4 − 2x^2 + 3.(a) Find all critical points and use the First Derivative Test to…

A: Given information:The given function is shown below:

Q: . How many point(s) of inflection are on che graph of f(x)=18x^3+5x^2-12x-17 * f(x) = 18x + 5x² -…

A:

Q: 22. (a) Find the critical numbers of f(x) = x*(x – 1)°. (b) What does the Second Derivative Test…

A:

Q: Suppose h is a twice-differentiable function such that it has second derivative given by the formula…

A:

Q: # 22 A right circular cone of radius 6m and height 10m is initially filled with water. An empty…

A: We know volume of water in cylinder = volume of cone - volume of water remaining in cone

Q: Here is the graph of the function h(x)on the interval (-5, 5), and part of a line tangent to h(x) at…

A:

Q: 2. Let f: (0,-1→ R be a function defined by f (x) = x¯* for every x E (0,-1. Sketch its function…

A: This is a problem of the application of differential calculus.

Q: 3. Iff has a local maximum at x – 1, then what can you say about f'(1)? What if you also know that f…

A: Given: The function fx has a local maximum at x=1. First derivative test: Let f be differentiable…

Q: 1 Sketch a graph of the function f(x) = 3 sin 5- 4- -87T -7 -6I -5 -47T -37 -27 27T 37T 47T -2- -3…

A: the amplitude of the function is 3 the time period of the function is  2π1/4=8π

Q: 3) State the critical points of the function g(x) = (x – 9) 23

A: A critical point occurs when the derivative is 0 or undefined.

Q: 1 4. Find the maximum value of f (x) = In(x- Inx) on the interval-<x<e. e

A: Given problem:- Find the maximum value of ƒ (x) = ln(x−lnx) on the interval 1/e≤x≤e

Q: Find the exact global maximum and minimum values of the function. f (x) x- lnx for x > 0 If there is…

A: We need to find the global maximum and minimum values of f(x), where f(x) is given by,

Q: 6. Sketch an even continuous function with all of the following features: ✔✔✔✔ • Absolute maximum at…

A: We have to draw graph with given information.  Even function means symmetric about y axis.  Y…

Q: 3. Find all -values where the graph of f(x) = x³ + 3x² + x + 3 has a horizontal tangent line.

A: Solution is given below:

Q: b- find any locl maximum and locl minimum values by using first derivative: f(x)=x-2x²

A: We can use application of derivative order to solve the given problem.

Q: -) Graph Y = 3*2), show critical points, where graph crosses the “X" & “Y" axes.

A: Making the graph of function we can see that graph cuts y axis and is an asymptote to x axis as…

Q: 1 The equations of the vertical asymptotes of the function with rule f (0) = are: 1+ cose

A:

Q: 7. What does the critical point(s) mean to the graph of the function? Determine the critical…

A: Critical points of graph of function points on graph of function where derivative is zero or…

Q: b- find any locl maximum and locl minimum values by using first derivative: f(x)=x*-2x²

A: Points of local extremum can be calculated by using the first derivative. These are points which…

Q: 6. Find the length of the curve given by the graph of the function f(x) = x/x, for x in [1,4].…

A:

Q: EXAMPLE 6 Discuss the curve y = 3x* - 48x³ with respect to concavity, points of inflection, and…

A: If fx=3x4-48x3, thenf'x=12x3-144x2=12x2x-12f''x=36x2-288x=36xx-8 To find the critical numbers we set…

Q: | 1) Find a function y whose graph passes through the point (1, ) and satisfies x²y' = y.

A:

Q: Find the exact global maximum and minimum values of the function. 1 for x 0 f (x)x х If there is no…

A: Given,

Q: 17 The function f is defined by f(x) = 5x - c, where c is a constant. In the xy-plane, the graph of…

A: Solve both the problem in the following way:- (i) given point will satisfy the function. (ii)…

Q: 13.Find a sinusoidal function with a maximum value of 9 that occurs at x=4 , and a minimum value of…

A:

Q: Suppose the graph of f(x) = x3is compressedvertically using a factor of 1/3and then shifted to…

A: Given : The parent function is f(x ) = x3 . The graph of f(x) = x3 is compressed vertically using a…

Q: Suppose that the function y=f(x) is increasing on the interval (-1,5). Over what interval is the…

A: The x-5 is offsetting the input of x. The beginning of the function increase is at x-5=-1 and the…

Q: 12. The graph on the right is NOT differentiable at x = 1. For what reason is it not differentiable?

A: Yes, given graph is correct.Given function:f(x) = x-1f(x) = -x+1        x&lt;1x-1           x≥1

Q: 3. To achieve the maximum benefit for the heart when exercising, your heart rate (in beats per…

A:

Q: Shown is the graph of the derivative f'(x) of the function f(x). (a) Identify the critical numbers…

A:

Q: 4. Find the point on the graph of f(x) 5x + 20x – 3 where the tan gent line is horizontal. 5

A:

Q: 3. Give an example of a function with discontinuities at x =1 and x = 5.

A: To Find : A function that has discontinuities at x=1 and x=5.

Q: Sketch the graph of a differentiable function y f(x) through the point (-2,2) if f'(-2)=0 and…

A: Given: To sketch the graph of the differentiable function function y=f(x) through point (-2, 2) if…

Q: 13. Find the minimum and maximum value of the function on the given interval. y = 2x 2 + 4x + 5 [-2,…

A:

Q: On the graph of f(x)=cosx and the interval [−2π,0), for what value of x does f(x) achieve a minimum?

A: We know,  -1≤cos x≤1 for any real value of x.

Q: 8. Determine a quadratic function f(x) = ax² + bx + c if its graph passes through the point (2,22)…

A:

Q: A function y = f(x) is decreasing on the interval [0, 5]. What conclusions can you draw about the…

A: A function is increasing, if when x increases, the value of y also increases.          Since the…

Q: (1) Find the derivative of the function f(x) = 2x³ - 12x² +4 and use it to find the critical numbers…

A: Solution is given below:

Q: Investigate the connections between key properties such as increasing/decreasing intervals, local…

A:

Q: Limit x approaches to + infinity 3x+1 ÷ 2x-5

A: To evaluate: limx→∞3x+12x-5 Solution: Here,limx→∞3x+12x-5 On simplifying further we get:…

Q: 3. Consider the function f(x) = r - 1+x 1- a. Explain why, when evaluated in a floating point…

A: