Respuesta :

leena

Hello!

[tex]\large\boxed{a = -1}[/tex]

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

Space

Answer:

a = -1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

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:

  • f(x) = cxⁿ
  • f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

y = 2x³ + ax² - x + 3

y'(1) = 3

Step 2: Differentiate

  1. Basic Power Rule:                    y' = 3 · 2x³⁻¹ + 2 · ax²⁻¹ - 1 · x¹⁻¹ + 0
  2. Simplify:                                    y' = 6x² + 2ax - 1

Step 3: Solve for a

  1. Substitute:                         3 = 6(1)² + 2a(1) - 1
  2. Exponents:                        3 = 6(1) + 2a(1) - 1
  3. Multiply:                             3 = 6 + 2a - 1
  4. Combine like terms:         3 = 5 + 2a
  5. Isolate a term:                   -2 = 2a
  6. Isolate a:                            -1 = a
  7. Rewrite:                             a = -1

Otras preguntas