Question

Let f(x) = x + sin(x) Every point on the graph is rotated by 45 degree with respect to the origin along the radius equal to the radius vector at that point. How many c that belong to [0, 11π] exist Such that f'(c) = 0.

(a) 10

(b) 11

(c) 110

(d) 9

I had been asked this question in an online quiz.

Question is from Rolle’s Theorem in portion Differential Calculus of Engineering Mathematics

Answer 1

Right option is (b) 11

For explanation I would say: The function has the beautiful property that the sine function is built over the line y = x

In other words the axis for the sine graph is no more on the x axis but is the line y = x.

When this graph is rotated by 45 degrees which Is equal to the slope of the line y = x we must get the original graph sin(x) again. The number of c in the interval [0, 11π] is then obviously equal to eleven.