Question

If \( (2, a) \) and \( (b, 19) \) are two stationary points of the curve \( y = 2x^3 - 15x^2 + 36x + c \), then \( a + b + c = \dots \)

• A. \( -20 \)
• B. \( 15 \)
• C. \( -12 \)
• D. \( 24 \)

Hint:

For stationary points, differentiate the equation of the curve and solve for where the derivative equals zero. Then substitute back into the original equation.

Answer 1

The Correct Option is B

We are given the curve equation \( y = 2x^3 - 15x^2 + 36x + c \) and that \( (2, a) \) and \( (b, 19) \) are stationary points. Step 1: To find stationary points, take the derivative of the equation: \[ y' = 6x^2 - 30x + 36 \] At stationary points, \( y' = 0 \), so solve for \( x \) when \( y' = 0 \). Step 2: Substitute \( x = 2 \) and \( x = b \) into the derivative equation and solve to find \( a \) and \( b \). Step 3: Use the equation for the curve to solve for \( a \), \( b \), and \( c \). After solving, we find \( a + b + c = 15 \). % Final Answer The value of \( a + b + c \) is \( 15 \).