Calculus · SEC2_GYM

Curve analysis and optimisation

Question 1/8+12 XP

For : what is the local slope at ?

Secant becomes tangentf(x) = 6x³, x = 1

curve fsecant Δx = 0.6secant Δx = 0.3secant Δx = 0.1tangent, slope 18point of tangency

All three secants pass through (1, 6). As Δx shrinks (0.6 → 0.3 → 0.1) the secant slope moves 30.96 → 23.94 → 19.86 — towards the tangent slope f′(1) = 18. That limit is the derivative.

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