4 The gradient of the tangent line to the graph of f(x) = 3x2 - 2kx-9 at x = 1 is 10. Find the value of k.

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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4 The gradient of the tangent line to the
graph of f(x) = 3x² - 2kx-9 at x = 1 is 10.
Find the value of k.
7 Let f(x) = Sax³ - 2bx² + 4cx.
Find f'(x).
Given that f'(x) ≥ 0 and a > 0, show that
b2 ≤ 15ac.
a
b
Transcribed Image Text:4 The gradient of the tangent line to the graph of f(x) = 3x² - 2kx-9 at x = 1 is 10. Find the value of k. 7 Let f(x) = Sax³ - 2bx² + 4cx. Find f'(x). Given that f'(x) ≥ 0 and a > 0, show that b2 ≤ 15ac. a b
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