Chapter 4 Multiple choice questions

* not completed

. Which of the following is not true about the derivative, dy/dx, of a function, y = f(x) ?

The function must be continuous for it to exist. correct incorrect

The function must be smooth for it to exist. correct incorrect

It gives the slope, or gradient, of the function. correct incorrect

It is equal to the sine of the angle of the slope. correct incorrect

* not completed

. If y = e^-x cos(x²), what is dy/dx ?

[ – cos(x²) – 2x sin(x²) ] e^-x correct incorrect

[ – cos(x²) + 2x sin(x²) ] e^-x correct incorrect

[ cos(x²) – sin(x²) ] e^-x correct incorrect

[ cos(x²) + sin(x²) ] e^-x correct incorrect

* not completed

. If y = x ln(x) + exp(-x²), what is dy/dx ?

ln(x) + exp(-x²) correct incorrect

ln(x) – 2x exp(-x²) correct incorrect

1 + ln(x) – 2x exp(-x²) correct incorrect

1 + ln(x) + exp(-x²) correct incorrect

* not completed

. What is the lowest value of y for the function y = x² [ 3x² – 4x – 12] ?

0 correct incorrect

-5 correct incorrect

-32 correct incorrect

Unbounded, tends to minus infinity. correct incorrect

* not completed

. What is the nature of the stationary point that has d²y/dx² = 0 ?

It is a maximum. correct incorrect

It is a minimum. correct incorrect

It is a point of inflexion. correct incorrect

Any of the above is possible. correct incorrect