56. a. Graph f(x) = Vx – 2. b. From the graph of f, is fa one-to-one function? c. Write the domain of fin interval notation. d. Write the range of fin interval notation. e. Write an equation for f(x). f. Explain why the restriction x 0 is placed onf. g. Graph y = f(x) and y = f'x) on the same coordinate system. h. Write the domain of f in interval notation. i. Write the range of f in interval notation.

Q: 6.) Use the limit definition of the derivative to find f' (x), given f(x)=x-3 x+5

A: Consider the function

Q: 30. Consider the function defined by 0ifx 1 Sketch this graph and find all points where the graph is…

A:

Q: 2. Let f (x) = x² + 3x – 5. а. Use the formal limit definition of the derivative to compute f'(x).

A: Given,          fx=x2+3x-5

Q: Suppose f is a function where the line tangent to it at x = 3 is given by y = 5x + 2. Find the…

A: Given information: y=5x+2,  Find the value of f(3) and f'(3)

Q: Suppose that f is a function given as f(x)=x3+bx2+cx−4 Find the exact values of b and c if we know…

A: Given: fx=x3+bx2+cx-4   and tangent line y=36x+68

Q: 2. Given the function f(x) = ., determine if the function is continuOus or not. Identify the point/s…

A: Given function f(x)= (x2-1)/(x-1) is continuous or not , determine type of discontinue.

Q: 1. Given the graph of f', the derivative of f, locate all extrema of f. JUSTIFY. Minimum at x =…

A: To find the minima and maxima from the graph of f'(x)

Q: 9. Show that for f(x) = x° we have f"(0) = 0 but the point x = 0 is not an inflection point of f.

A:

Q: F(X)

A: y = f(x) is continuous at x = a  only if following properties are satisfy : (1)  f(a) exists . (2)…

Q: Find the value of the constant bl that makes the following function continuous on (-∞, ∞). if x 6|…

A:

Q: Suppose that the di’erentiable function y = g(x) has an inverseand that the graph of g passes…

A: Differentiable function y=g(x) ha an inverse ; Graph of g passes through the origin with slope 2;

Q: 51. Is the function given by G(x) 1 continuous at x = 0? Why or why not?

A: Given: Gx=1x To check whether the given function is continuous at x=0

Q: Find a function f such that f (x) = 2x3 and the line 54x + y = 0 is tangent to the graph of f. f(x)…

A: Key point used: The slope m, of the tangent to f(x) at point h,k, is equal to f'x=h. Given:Eq of…

Q: At what points is the function is continuous y=|2x-1| +4sin(2x)

A:

Q: For which values of x is the function below NOT continuous?

A: To find out the values of x at which the function is discontinuous.

Q: Find the limit of the function as x approaches −1.x^2−4x−5x/x+1limx(→−1)f(x)=

A: Given,

Q: The graph of f(x) and a line tangent to the curve at x = 4 are shown. If g(x) = f(x), evaluate…

A: Finding the g'(4) from the given conditions.

Q: Suppose that flx) is a differentiable function and g(x)=(x+2)/f(x). If f(0)= 22 and f(0)=5, then…

A:

Q: Find a function f such that  f '(x) = 5x3  and the line  135x + y = 0  is tangent to the graph of…

A: Consider the given derivative function f'x=5x3

Q: 1. Use the limit definition of the derivative to find g'(x) if g(x) = 2x² – 6x + 13.

A:

Q: Suppose that f is a continuous function such that | f(x) dz = -12. Find | () dr.

A:

Q: Find k such that the line is tangent to the graph of the function.

A: The function is given as fx=kx......(1) The line is given as y=x+4......(2)

Q: calculate the are between the curves f(x)=x^2 and g(x)=x^3 on the interval [-1,1]

A: Given,

Q: Find a function f such that f'(x) = 2x³ and the line 54x + y = 0 is tangent to the graph of f. f(x)…

A:

Q: Suppose g is the function defined by picture where k and m are constants. If g is differentiable at…

A: Solution

Q: 2. Use the graph of the function f(x) to estimate where (a) f'(x)= 0, y f(x) (b) f'(x) 0.

A: (a) f'(x) =0   => the slope is zero, it means when the graph is parallel to x-axis  i.e. at…

Q: Is the function given by g(x) = x²-3x continuous at x = 4? Why or why not?

A:

Q: For function f (x, y) x2+1 Let us consider the level curve f(x, y) = 2. Does the point (1, 2) belong…

A: f(x,y) = y2/(x2+1)  Also,  f(x,y) = 2  We have (x,y) = (1,2)

Q: 2. Use the limit definition of derivatives to find the expression for f'(a) for the function 1 f(x)…

A: Here ,               We have given a function now we have to solve it by using definition of limit…

Q: Use the four-step definition of the derivative to find f'(x) if f(x) = 5x 4. f(x + h) = f(x + h) –…

A:

Q: 2, if x 1

A: The given function,  f(x)=1x,if x≤1x2-1,if x>1

Q: Suppose that f(x) is a differentiable function and g(x)=(x+2)/f(x). If f(1)= 5 and f'(1)=10, then…

A:

Q: Suppose that f is a continuous function such that | f(x) dz = -12. Find (*") dr.

A:

Q: Find for the following function: 1- y = etan'x 2-x'y+ x*y 2 at x = 2

A:

Q: 1 Find the distance between the two values of x at which the function is discontinuous. x²-3x + 2

A: The function given is ,f(x) = 1x2-3x+2f(x) is discontinous when,x2-3x+2 = 0Using quadratic formula,x…

Q: Let f=3x^2+2 and find the values below 1) f(x+h) 2) (f(x+h)-f(x)) 3) lim h→0 (f(x+h)−f(x))/h 4) Find…

A: The given function is f(x)=3x^2+2.

Q: Let f(x) = 2x² 11a + 4 - The slope of the tangent line to the graph of f(x) at the point (2, 10) is…

A: This is a problem related to derivative of the function. Please follow the procedure given below.

Q: Find a function f such that f'(x) = x4 and the line 2x - y = 3 is tangent to the graph of f.

A: Given that

Q: The graph of  f(x)  and a line tangent to the curve at  x = 4  are shown. If  g(x) = sqrt(f(x))…

A: In the question it is asked to calculate the value of g'(4) for g(x)=f(x). for the graph given…

Q: Find the value of the constant cc that makes the following function continuous on (−∞,∞)(−∞,∞).…

A: We have been given a piecewise function and we need to determine the value of ‘c’ at which the given…

Q: The graph of the derivative f' of a continuous function f is shown. (Assume f' continues to o.) y y…

A: Given that: Graph of f'(x)

Q: For f(x) = 2x2 +1, use the definition of the derivative f'(x) = lim (e+h)-}(=) to find f'(x). h0 h O…

A: f(x) is differentiable then  h→0limf(x+h)-f(x)h Here f(x)=2x2+1

Q: 6. Determine the inflection points and intervals of concavity for the function y= e2*

A:

Q: Consider the following function. f(x) = x* + 4x3 + 11 (a) Make a sign diagram for the first…

A: We have to find the sign diagram for first derivative,  sign diagram for second derivative,  sketch…

Q: 14) What is the domain of the function f(x) E, ?

A:

Q: Start with g(x) = 3x. Use the limit definition of the derivative to show what g'(x) is.

A:

Q: What is the x-value associated with the extreme point of the following function: 1*1.1^x+ 1*0.2^x?

A: Given Data: Function: fx=1×1.1x+1×0.2x The derivative of the given function is,…

Q: Find a function f such that f '(x) = 5x3 and the line 40x + y = 0 is tangent to the graph of f. f(x)…

A:

Q: Find a value for the constant k, if possible, that will make the function continuous. kox+1 for x 3

A: K = 1/3