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Find the derivative of f(x) = 3x⁴ - 2x² + 5x - 7 and evaluate at x = 2
calculus_assignment.pdf
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I'll solve this step-by-step using calculus principles:
Step 1: Apply the power rule for each term
f'(x) = 3 · 4x³ - 2 · 2x¹ + 5 · 1x⁰ - 0
For each term of form ax^n, the derivative is a·n·x^(n-1)
Step 2: Simplify the expression
f'(x) = 12x³ - 4x + 5
Multiply the coefficients and reduce the exponents
Step 3: Evaluate at x = 2
f'(2) = 12(2)³ - 4(2) + 5
Substitute x = 2 into the derivative expression
Step 4: Calculate the result
f'(2) = 12 · 8 - 8 + 5 = 96 - 8 + 5 = 93
Compute the final value through order of operations
Final Answer
The derivative f'(2) = 93
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