In Exercises 5-8, use the definition f'(a) = lim x→a f(x) = f(a) to find the derivative of the given function at the given value of a. 6. f(x) = x² + 4, a = 1 8. f(x) = 2x + 3, a = = −1 = 1/x, a = 7. f(x) = √x + 1, a = 3 9. Find f(x) if f(x)= 3x - 12. 10. Find dy/dx if v = 7 2 x - a

Q: For each of the above functions, prove that f(f-1(x)) = f-1(f(x)) = f(x) = +6 f(x) = x3 + 2 f(x)…

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Q: Let f(x) = *+3_ 2x + 1 a. Find a function formula for f-'(x), the inverse function of f. Show your…

A: For inverse function put f(x)= y and find x in terms of y , that will be inverse of f(x) , now  For…

Q: f(x) = |x| · : %3D Then f-l(x) = if x > 0, and f-l (x) = if x < 0.

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Q: Graph of polynomial f(x)

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Q: Set f(x)= sin x. Show that finding f'(0) from the definition of derivative amounts to finding sin x…

A: f(x) = sinx

Q: If f(x) = 6x²e*, then what is the derivative of f(x) with respect to x? 6xex O 12xe* О бхе"(x + 1) O…

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Q: 3. Use the graph of y = f(z) to sketch the graph of its derivative f'(x). -2 -1 16- 12+ 8 4+ ܕ <-4…

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Q: Consider the following function. f(x) = x* - 16x3 + 72x2 + 2 (a) Make a sign diagram for the first…

A: Using first derivative test.

Q: / Discuss the relationship between the derivative and (Lim) with drawing if it is required?

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Q: In Exercises 45-74, compute the derivative using derivative rules that have been introduced so far.…

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Q: Let f(x) be a polynomial function, whose derivative is given by f'(x). Let line q be the line…

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Q: Explain and sketch how a function can have f ''(a) = 0 at (a, f(a)) and not be an inflection point.

A: It is given that f''(a)=0 at (a, f(a)). The objective is to explain and sketch how a function can…

Q: 1. Use the Power Rule and properties of derivatives to find the derivative of each function a) f(x)…

A: Here we have to find the derivative by using power rule and the properties of the derivative.

Q: Example: Give an example of a function and a value a so that f"(a) = and (a, f (a)) is not an…

A: The objective is to give an example of a function and a value a so that f"(a)=0 and (a,f(a)) is not…

Q: Let f be a function defined by: f(x) = ln(22x). In Then, f-¹(x) = e¯* + 2. ос إختر واحداً: True…

A: Topic = Functions TRUE

Q: b\ State and prove the theorem of (derivative of inverse functions), then use it to answer these…

A: We have to find the derivatives of the functions

Q: Suppose that f is a function given as f(x) = 2x² + 7x - 2. Simplify the expression f(x + h). f(x +…

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