The gradient of the tangent of the curve y=2x^3 + ax^2 - x + 3 at the point x=1 is 3. Find the value of a.

Hello!

y = 2x³ + ax² - x + 3

Find the derivative using the power rule:

y' = 6x² + 2ax - 1

Substitute in the given slope and x value to solve for a:

3 = 6(1)² + 2(1)a - 1

3 = 6 + 2a - 1

4 = 6 + 2a

-2 = 2a

a = -1

a = -1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Calculus

The definition of a derivative is the slope of the tangent line.

The derivative of a constant is equal to 0.

Basic Power Rule:

Step-by-step explanation:

Step 1: Define

y = 2x³ + ax² - x + 3

y'(1) = 3

Step 2: Differentiate

Step 3: Solve for a

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