QCEVault

Differentiation of exponential and logarithmic functions — Question 271

Original QCE Vault practice · 4 marks

Q271 · Practice questionTechnology-freeComplex familiar4 marks

QUESTION 271 (4 marks)

The curve y=ln⁡(2x+1)y=\ln(2x+1) is defined for x>−12x>-\dfrac12.
Graph of y=ln(2x+1), with its tangent at the origin drawn as a dashed line.
a)
Determine the gradient at x=0x=0.
[1 mark]
b)
Determine the equation of the tangent at x=0x=0.
[1 mark]
c)
Use the second derivative to explain why this tangent lies above the curve throughout its domain.
[2 marks]
Question linkSyllabus coverage

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