Estimate graphically the local maximum and local minimum of f(x) = 4x2 + 3x + 2

Mathematics

2 answers:

Juliette [100K]3 years ago

6 0

Hope this helps you. If you need any help regarding how to sketch graph, ping me

jarptica [38.1K]3 years ago

4 0

Seeing the graph from desmos.com, we know there is only one place where the graph will go up then down, or down then up given that the maximum exponent of x is it squared. That place, as seen, is -0.375 for the minimum as it goes down then up. There's no maximum in sight :(

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Answer: $\bold{a)\quad 90\sqrt2\qquad \qquad b)\quad 45\sqrt2}$

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Since you are looking for the distance from home plate to second base, you are actually looking for the length of the diagonal of the square. Use the Pythagorean Theorem: a² + b² = c² where a and b are the side lengths and c is the length of the diagonal.

$90^2+90^2=c^2\\8100+8100=c^2\\16200=c^2\\\sqrt{16200}=c\\\boxed{90\sqrt2}=c\qquad \qquad \text{which is approximately 127.28}\\\\\\\\\text{Halfway between home plate and 2nd base means divide that length by 2:}\\\\\dfrac{90\sqrt2}{2}=\boxed{45\sqrt2}$