## 5.2 Increasing decreasing Functions

Calculator Allowed: Yes Question Answer Transcription of this question: [Maximum mark: 151Let f (x), for(a)(b)(c)(d)Sketch the graph Of(i) Write down the x-coordinate Of the maximum point on the graph Of f.(ii) Write down the interval where f is increasing.20-6xShow that f'(x)Find the interval where the rate Of change Of f is increasing.[3 marks][3 marks][5 marks][4 […]

## 5.2 Increasing decreasing Functions

Calculator Allowed: Yes Question Answer Transcription of this question: 5.[Maximum mark: 61The population Of deer in an enclosed game reserve is modelled by the functionP (t) = 210sin (0.5t —2.6) + 990 , where t is in months, and t = I corresponds to I January 2014.(a)(b)Find the number Of deer in the reserve on […]

## 5.2 Increasing decreasing Functions

Calculator Allowed: No Question Answer Transcription of this question: [Maximum mark: 7]Consider the function defined by f (x) = x’— 3×2+ 4.(a) Determine the values of x for which f(x) is a decreasing function.There is a point of inflexion, P, on the curve y = f(b) Find the coordinates of P.

## 5.3 Derivative of a Function

Calculator Allowed: No Question Answer Transcription of this question: [Maximum mark: 6]4.Part Of the graph Of f (x) — 6×2 is shown below.The point P lies on the graph Of At P, x —l(a)(b)Find TThe graph Of f has a gradient Of 3 at the point P.Find the value Of a.[2 marks][4 marks]

## 5.3 Derivative of a Function

Calculator Allowed: No Question Answer Transcription of this question: [Maximum mark: 7]7.Let f (x) = px3 +Given that f’ (x) 20, show that p2 < 3pq(a)(b)Find f' (x)[2][5]

## 5.3 Derivative of a Function

Calculator Allowed: No Question Answer Transcription of this question: [Maximum mark: 6]Let f (x) =(a) Write down f'(x) , f “(x) , and .(b) Find an expression for f (“i

## 5.3 Derivative of a Function

Calculator Allowed: Yes Question Answer Transcription of this question: [Maximum mark: 5]Let f (x) — In x — 5x, for x > O.(a)(b)(c)Find f'(x).FindSolve = f[2][2]

## 5.4 Equations of tangents and Normals.

Calculator Allowed: Yes Question Answer Transcription of this question: 6.imum mark: 7]Consider the curve y = In (3x—1). Let P be the point on the curve where x — 2(a)(b)Write down the gradient of the curve at PThe normal to the curve at P cuts the x-axis at R. Find the coordinates of R.[5 mam*s]

## 5.4 Equations of tangents and Normals.

Calculator Allowed: Yes Question Answer Transcription of this question: 5.[Maximum mark: 71Consider the curve with equation f (x) + qx, where p and q are constants.The point A (1, 3) lies on the curve. The tangent to the curve at A has gradient 8.Find the value Of p and Of q.

## 5.4 Equations of tangents and Normals.

Calculator Allowed: No Question Answer Transcription of this question: 3.[Maximum mark: 6]Let f (x) e x cosx. Find the gradient Of the normal to the curve Of f at