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Daniel J Smith Custom TMUA Set A Paper 2 · Q9

Paper 2Functions & graphsAlgebra

Let f(x)=ax2+bx+cf(x)=ax^2+bx+c be a quadratic function with real coefficients such that f(x)≥0f(x)\geq0 for all real xx

Suppose that for every real xx,

f(x+1)−f(x)≥2x+3f(x+1)-f(x)\geq2x+3

What is the smallest possible value of f(0)f(0)?

A00
B14\frac14
C11
D22
E94\frac94
F44
G254\frac{25}{4}

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