Calculus & Vectors (MCV4U) · Curve Sketching Optimization

Critical Points and the First Derivative Test

10 tutor-authored questions for this Ontario curriculum expectation, ordered easiest to hardest — every one with a full worked solution. Work through them free, no account needed.

Start the 10 questions Curriculum: MCV4U-CSO.1

Sample: the first question, solved

Find the critical point of f(x)=x²−6x+8.

📘 Worked solution
f'(x)=2x−6. Setting f'(x)=0 gives 2x−6=0, so x = 3.

And one from the hard end

Find the critical points of f(x)=x³−3x²−9x+5.

Solution shown after you try it in practice mode.

Work through all 10, easiest to hardest

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