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What is the value of $x$ if $3x + 5 = 14$?
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Static Image/Diagram Needed: A graph of the parabola f(x) = x^2 - 4x + 7. Clearly mark the vertex (minimum point) and its coordinates (2, 3). Also show the tangent line at the vertex, which should be horizontal.
(Keywords: parabola, quadratic function, derivative, minimum, vertex, tangent line)
Consider the function $f(x) = x^2 - 4x + 7$.
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Find the derivative $f'(x)$.
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At what value of $x$ does $f(x)$ have a local minimum?
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What is the value of this local minimum?
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Static Image/Diagram Needed: The area under the curve of the function f(x) = 3x^2 + e^x from x=0 to x=1, shaded to represent the integral. The x and y axes should be labeled.
(Keywords: integral, area under curve, calculus, e^x, x^2)
Evaluate the integral $\int_0^1 (3x^2 + e^x) dx$.
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A box has dimensions: length $l=5$ units, width $w=3$ units, and height $h=2$ units. Calculate its volume and surface area.
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SVG Diagram Needed: A 3D representation of a rectangular box with dimensions labeled: length = 5, width = 3, height = 2. Use different colors for each face.
(Keywords: rectangular box, volume, surface area, 3D shape, dimensions)
This is a sub-question to illustrate parsing, even if Q4 wasn't originally nested.
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Static Image/Diagram Needed: A number line showing pi (approximately 3.14) and e (approximately 2.72). Illustrate the floor function applied to pi (resulting in 3) and the ceiling function applied to e (resulting in 3), then their sum, 3 + 3 = 6.
(Keywords: number line, pi, e, floor function, ceiling function)
What is $\lfloor \pi \rfloor + \lceil e \rceil$?