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How to solve this linearization problem?
Find the linearization of f(x) = cos^(2)(x) at a = π/4. Use this to approximate cos^(2)((25π+1)/(100)).
1 Answer
- Kathleen KLv 76 years ago
f(π/4) = cos²(π/4) = (√2/2)² = ½ ← point of tangency is (π/4, ½)
f '(x) = 2cosx∙-sinx = -sin(2x)
f '(π/4) = -sin(π/2) = -1 ← slope of tangent line (i.e. linear approximation)
y - ½ = -(x - π/4)
y = -x + π/4 + ½
When x = (25π + 1)/100,
y = -(25π + 1)/100 + π/4 + ½
y = -π/4 - 1/100 + π/4 + ½
y = 49/100
