Question

The number of values of c such that the straight line 3x + 4y = c touches the curve `x^4/2` = x + y is ______.

Options

• 0

• 1

• 2

• 4

Answer 1

The number of values of c such that the straight line 3x + 4y = c touches the curve `x^4/2` = x + y is 1.

Explanation:

y' = `(4x^3)/2 - 1`

2x³ – 1 = `-3/4`

8x³ = 1

x = `(1/8)^(1/3)` = `1/2` c has one value.