Using only the definition of concavity (that is, WITHOUT using derivatives! (or just looking at the graph)), show that y = such that 0 < a < b and follow the definition of concavity using the interval [a, b]. x3 is concave up for all x > 0. Start by saying that a and b are numbers

Q: (v) Let f(x) = /2x – 1, for r > 0. Use the definition of the derivative to compute f'(x).

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Q: use definition to show that the function f(x)= |x|^3 is differentiable at 0, with derivative equal…

A: We have to use definition of differentiable:

Q: 5. Why does it make graphical sense that the derivative of aconstant is zero? That the derivative of…

A: Derivative of a function is a slope of function on given point, or derivative is a rate of change of…

Q: the derivative of E(q) is-(q*(q^2-1))^-1. what's its global maximum and global minimum. Thank you!

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Q: By considering the derivative of the function f: [-1,1] → R defined by f(r) = show r2 +1' that f-1…

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Q: The fifth derivative of the function f(x) = 5x° is a constar False O True

A: Given query is to find statement is true or false.

Q: Use derivatives to find two positive numbers a and b such that: a^2 +b^2 = 1 and 2a+3b is as…

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Q: We are given that the derivative of a function f (z) at r = 2 is equal to f'(2) = 4. Which, if any,…

A: Explanation of the answer is as follows

Q: Use the alternative form of the derivative to find the derivative at x=c ( if it exists). f(x) =…

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Q: 2 Using the definition of derivative, prove the following: (a) f'(x) = x if f(x) = x %3D

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Q: 1. Let f(x) = mx + b, the line with slope m and y-intercept b. Use the rules of differentiation to…

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Q: QIFind the derivative of the function f(z, k) = z* – 16k + tanh(z) – 4 csc(k) in terms of z and k ?

A: Dear student  Here is the solution of your query

Q: 103. If fix) = r, n2 1, show from the definition of the derivative that f'(0) = 0.

A: The given function is fx=xn,  n&gt;1. Compute the derivative at 0 as follows.

Q: Supose z is implicitly defined by the equation qy+ 3x + xyZ + 32=9 in an enmrament of the point…

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Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. g(x) = 2x2…

A: Given function is gx=2x2-3x. We know that, f'x=limx→cfx-fcx-c Using the above formula of derivative,…

Q: Use the alternate form of the derivative to find the derivative at x=c, if it exists. f(x) = x³ +…

A: Given f(x) = x³ + 2x² + 1, c = -2 Find the derivative at x= c if exist by using the alternate form…

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

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Q: 4.x Suppose f(r) = if x >2 if x < 2 4 Find f'(2) using the definition of derivatives.

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Q: Use derivatives to find two positive numbers a and b such that a^2 + b^2 = 1 and such that 2*a+3*b…

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Q: The fifth-order partial derivative ∂5ƒ/∂x2∂y3 is zero for each of thefollowing functions. To show…

A: We have to find which variable should we choose so that we differentiate as quickely as possible.

Q: Suppose the derivative of f is f'(x) = (x + 1)*(x - 2)*(z- 3). On what interval is f increasing?…

A: A function f(x) is said to be increasing in an interval of it's derivative is positive in that…

Q: By considering the derivative of the function f : [-1,-1] → R defined by f(x) %3D r2 – x+1' 3. show…

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Q: g(u) u +1

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Q: Use the alternative form of the derivative to find the derivative at x = c (if It exists). f(x) = x2…

A: Given f(x)=x2-2 c=5

Q: Starting from the definition of derivative prove that if f(x) = 1 then f'(a) = a2

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Q: Find A and B given that the derivative of Ax? + B, x –1 is everywhere continuous.

A: Given function is f(x)=Ax2+B,x&lt;-1Bx5+Ax+4,x≥-1 We have to find the value of A and B  so that the…

Q: 2. (x² – y²)³ = 3a*x? %3D

A: The given equation is x2-y23=3a4x2 We have to find the derivative of y with respect to x. In this…

Q: Use the Quotient Rule to show that the Powers of x Rule appies to negative Integer powers. That s,…

A: The given function is fx=1xk   where k&gt;0. Quotient rule says that ddxfg=gdfdx-fdgdxg2.

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. g(x) = (x…

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Q: Suppose h(x): . What is the correct result of the derivative of h with respect to x? 3x · In (5)…

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Q: In the interval 3 < x < 4 of the first derivative test, f(x) is a. Not moving b. Changes direction…

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. In x 20) у 3

A: Given

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. f(x) = (x…

A: Given function is fx=x-623. To find the derivaitve of the function at x=c. Differentiating with…

Q: It costs Sugarco 25¢/lb to purchase the first 100 lb ofsugar, 20¢/lb to purchase the next 100 lb,…

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Q: Suppose that g: R →R is a differentiable function, with derivative g'(x)=(x – 1)·(x – 2)² - (x – 3)³…

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Q: d) Hence form a conjecture for the derivative of functions in the form y = (ax + b)². e) Prove your…

A: As you have mentioned I am answering Question (d) and Question (e)

Q: 2. Using the definition of derivative, prove the following: 1 (a) f^(x)= if f(x) = Vx %3D

A: fx=x3

Q: Find f'(a) using the definition of the derivative at a point for f(x) = 1 VI at a = 7.

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Q: Find the derivative of ?, implicitly of  BY SHOWING ALL STEPS When N=11 and M=3

A: Given that lnMxy-tanNx+My=e-M-MyN And N=11 and M=3

Q: Find the derivative of f (x) = coth³( In(x³)). -9coth (In(x³)) csch²(In(x³)) A B - 9x?coth ( In(x³))…

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Q: Use derivatives to find two positive numbers a and b such that a^(2)+b^(2)=1 and such that 2a+3b is…

A: Solved below

Q: Prove, by Showing all steps i that the 1. derivative of arcos x is 1-メ

A: Derivative of arccosx is -1/√(1-x2)

Q: Use the u-substitution to find the anti-derivative of h'(x)= xcos(2-3x2)

A: h'(x)=xcos(2-3x2) Formula ∫cos (x) dx= sin (x)+C

Q: Show that the function f(z) does not admit an anti-derivative in the domain N = C\{0}. Does it admit…

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Q: The fifth-order partial derivative ∂5ƒ/∂x2∂y3 is zero for each of thefollowing functions. To show…

A: fx, y=x2+5xy+sinx+7ex Since the given function consists of 3 terms in terms of x namely x2,  sinx…

Q: Using the definition of the derivative, find f (x), if f(x)=mx+b where m,b are real.

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Q: The derivative of Q with respect to r for: Q=In (r+1)' is: 2)

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: