Derivatives review

Tuesdays quiz task...

Reviewing what happens when the save button lies

By Connor Buddy

Apologies for the absence

Lets review

Multiple Choice

Determine the instantaneous gradient/rate of change of the curve with equation $$y=x^2-4x+5$$ at the following points. (a) (2,1) (b) (-1,10)

• (a) 0, (b) -6

• (a) 4, (b) -6

• (a) 0, (b) 6

• 
  (a) 4, (b) 6

Math Response

State the equation of the tangent at the following stationary point

Type answer here

Correct Answer: y=4

Deg^°

Rad

Math Response

Type answer here

Correct Answer: x=-2

Deg^°

Rad

Graphing

A curve C has equation $$y=x^2-4x+3$$ . A point A (1,0) lies on the curve. Determine the equation of: The normal at a in the form of:

2y= mx + c

Multiple Choice

The tangent to the curve with equation $$y=x^3+3x^2-2x$$ at the point A has gradient 22. Given that x>0 for the point A, determine the x-coordinate of A.

• 1

• 2

• 3

• 4

Multiple Choice

A curve has equation $$y=2x^2+3x-9$$ 9. At a point P on the curve, the tangent is parallel to the line y=4−5x . What are the coordinates of P?

• 
  (-1, -10)

• 
  (1, -4)

• 
  (-2, -7)

• 
  (-2, -5)

Multiple Choice

A curve with equation y=f(x) passes through the point (4,25). f(x)= $$\frac{1}{8}x^3-20x^{\frac{1}{2}}+x+53$$ where x≥0 . Find an equation of the normal to the curve at the point (4,25).

• $$y=-\frac{1}{2}x+27$$

• $$y=\frac{1}{2}x+23$$

• $$y=-2x+33$$

• $$y=2x+17$$

Multiple Choice

The point P on the curve $$y=6\sqrt[]{x}$$ has x-coordinate 4. The normal to the curve at P is parallel to the line $$2x+3y=0$$ . This normal meets the x-axis at the point Q. Calculate the area of the triangle OPQ, where O is the point (0,0).

• 132 square units

• 54 square units

• 30 square units

• 24 square units

Math Response

The diagram shows the graph with equation $$y=x^3-6x^2+11x-3$$ . The tangent to the curve at A(1,3) intercepts the curve again at B. Hence find the coordinates of B, the point of intersection of this tangent with the curve.

Leave your answer in the form "(x.y)" using a full stop, they don't have commas!

Type answer here

Correct Answer: \left(4.9\right)

Deg^°

Rad

Multiple Choice

Determine the second derivative for each function. $$y=x^7−3x^6+2$$

• $$\frac{\text{d}y}{\text{d}x}=7x^6-18x^5$$

• $$\frac{\text{d}^2y}{\text{d}x^2}=42x^5-90x^4$$

• $$\frac{\text{d}^2y}{\text{d}x^2}=210x^4-50x^3$$

• $$\frac{\text{d}^2y}{\text{d}x^2}=42x^6-90x^5$$

Multiple Choice

Determine the second derivative of the given function at the specific point. $$f\left(x\right)=\frac{4+x^2}{2\sqrt[]{x}}$$ at (4,5)

• $$\frac{1}{16}$$

• $$\frac{12}{47}$$

• $$\frac{15}{64}$$

• $$-\frac{1}{8}$$

Math Response

[Edexcel IAL Mathematics Jan 2019 Pure 1 Q6b] Given $$f\left(x\right)=2x^{\frac{5}{2}}-40x+8$$ , x > 0, solve the equation $$f''\left(x\right)=5$$

Type answer here

Correct Answer: \frac{4}{9}

Deg^°

Rad

Poll

Rate your knowledge and current understanding of Differentiation so far

• 1 Star

• 2 Star

• 3 Star

• 4 Star

Now for an exam question to push you

Math Response

a) Factorise completely $$y=9x-x^3$$

Type answer here

Correct Answer: x\left(x-3\right)\left(x+3\right)

Deg^°

Rad

Dropdown

The line l has equation $$y=k$$ , where k is a constant.

Select answer

<k<​

Select answer