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Worked solution

Practise the point-slope tangent equation

Find the equation of the tangent to the curve y=3x2−4x+5y=3x^2-4x+5 at the point (1,4)(1,4).

CJC · Lecture · Self-Practice 2

Differentiate and substitute

The source prints only the final answer. Independently, dy/dx=6x−4dy/dx=6x-4, giving slope 2 at x=1x=1; the curve gives y=4y=4 there.

How did this part go?

Use the specified point

y−4=2(x−1)y-4=2(x-1) gives y=2x+2y=2x+2, matching the printed answer in both copies.

How did this part go?

Common mistakes

Use the derivative at x=1 as the slope, then use (1,4) to find the line’s constant term.

Solution notes

Both source copies visually compared; source wording, displayed results and pagination retained. Independently authored analytical explanations are distinguished from printed working.

Read the hint